Lemma 2.7 ([1]}) 
Let \(\lambda ,\mu \in {\mathbb {Y}}\)  and \(n\in {\mathbb {Z}}_{\ge 0}\) .
Using the notation (REF ) and (), we set
\(\ell =\ell (\lambda ),\qquad k=\ell (\mu ),\qquad \eta =r_n(\lambda ), \qquad \gamma =(r_n(\mu ^{\prime }))^{\prime },\\\tilde{\eta }={\left\lbrace \begin{array}{ll}\bar{\eta }, & n\le \ell -1,\\\big (\lambda ,1^{n-\ell +1}\big ), & n\ge \ell .\end{array}\right.}\) 
